Constructing a TRIX oscillator from daily declines

Noisy internals, not a freehand line

Daily advance and decline counts were treated as noisy series with large random fluctuation, and visual trendline breaks on an advance-decline cumulative line were judged too subjective for systematic use.

The indicator is constructed as the one-day rate of change of a triple exponential smoothing of the daily number of declining stocks. That daily number of falling listed issues is the decline-count: the raw input instead of closing price.

Three identical exponential-smoothing stages

After comparing lookbacks, each of the three exponential averages was set to 35 days as the length that appeared useful on the decline series.

Exponential-smoothing is a recursive average that mixes the latest observation with the prior smoothed value through a constant alpha, often estimated as two divided by one plus the chosen lookback. The exponential weight chosen to approximate a 35-day simple average is alpha equal to 2 divided by 36, or 0.05556, and that same constant is reused at every smoothing stage.

That single alpha is the smoothing-constant: reused at each of the three exponential stages so the stack stays internally consistent.

A one-day rate-of-change around zero

Trix is a one-period rate of change computed on a series that has already been exponentially smoothed three times with the same length or smoothing constant.

Rate-of-change is the period-to-period percent change of the fully smoothed series, used here to turn the third exponential average into a zero-centered oscillator. The oscillator value is the one-day percent change of the third exponential average: today's triple-smoothed value minus yesterday's, divided by yesterday's value, then multiplied by 100.

How the smoother is seeded

When an exponential average is started, the prior smoothed value is seeded with the first observation. Beginning the smoother on a different date can change later values slightly.

A long-only zero-line rule

The long-only rule attached to the 35-day decline oscillator was defined as entering when the oscillator falls below zero and closing the long when it crosses back above zero. Short sales were not taken from this series alone because of an upward market bias.

Four lengths and a large construction space

A one-day iterative search over four length variables from 2 through 60 days expands the construction space to 60 to the fourth power, or 1,296,000 combinations.